Using a suggested solution to speed up a process for simulating and correcting an integrated circuit layout

ABSTRACT

One embodiment of the invention provides a system for speeding up an iterative process that simulates and, if necessary, corrects a layout of a target cell within an integrated circuit so that a simulated layout of the target cell matches a desired layout for the target cell. The system operates by determining if the target cell is similar to a preceding cell for which there exists a previously calculated solution. If so, the system uses the previously calculated solution as an initial input to the iterative process that produces the solution for the target cell.

RELATED APPLICATION

This application is a continuation of pending U.S. patent application Ser. No. 10/098,714 filed on 15 Mar. 2002 by inventors Kevin D. MacLean and Roger W. Sturgeon, entitled “Using a Suggested Solution to Speed Up a Process for Simulating and Correcting an Integrated Circuit Layout” (Attorney Docket No. NMTC-0770). This application hereby claims priority under 35 U.S.C. § 120 to the above-listed parent patent application

The subject matter of this application is related to the subject matter in U.S. Pat. No. 6,795,955, by the same inventors as the instant application, entitled, “Method and Apparatus for Identifying an Identical Cell in an IC Layout with an Existing Solution” (Attorney Docket No. NMTC-0771).

BACKGROUND

1. Field of the Invention

The invention relates to the process of fabricating semiconductor chips. More specifically, the invention relates to a method and an apparatus for using a suggested solution to speed up an iterative process, such as optical proximity correction, for simulating and correcting a layout on a semiconductor chip.

2. Related Art

Recent advances in integrated circuit technology have largely been accomplished by decreasing the feature size of circuit elements on a semiconductor chip. As the feature size of these circuit elements continues to decrease, circuit designers are forced to deal with problems that arise as a consequence of the optical lithography process that is typically used to manufacture integrated circuits. This optical lithography process begins with the formation of a photoresist layer on the surface of a semiconductor wafer. A mask composed of opaque regions, which are formed of chrome, and light-transmissive clear regions, which are generally formed of quartz, is then positioned over this photo resist layer coated wafer. (Note that the term “mask” as used in this specification is meant to include the term “reticle.”) Light is then shone on the mask from a visible light source, an ultraviolet light source, or more generally some other type of electromagnetic radiation together with suitably adapted masks and lithography equipment.

This light is reduced and focused through an optical system that contains a number of lenses, filters and mirrors. The light passes through the clear regions of the mask and exposes the underlying photoresist layer. At the same time, the light is blocked by opaque regions of the mask, leaving underlying portions of the photoresist layer unexposed.

The exposed photoresist layer is then developed, through chemical removal of either the exposed or non-exposed regions of the photoresist layer. The end result is a semiconductor wafer with a photoresist layer having a desired pattern. This pattern can then be used for etching underlying regions of the wafer.

One problem that arises during the optical lithography process is “line end shortening” and “pullback”. For example, the upper portion of FIG. 1 illustrates a design of a transistor with a polysilicon line 102, running from left to right, that forms a gate region used to electrically couple an upper diffusion region with a lower diffusion region. The lower portion of FIG. 1 illustrates a printed image that results from the design. Note that polysilicon line 102 has been narrowed using optical phase shifting in order to improve the performance of the transistor by reducing the resistance through the gate region.

Also note that because of optical effects and resist pullback there is a significant amount of line end shortening. This line end shortening is due to optical effects that cause the light to expose more of the resist under a line end than under other portions of the line.

In order to compensate for line end shortening, designers often add additional features, such as “hammer heads,” onto line ends (see top portion of FIG. 2). The upper portion of FIG. 2 illustrates a transistor with a polysilicon line 202, running from left to right, which forms a gate region used to electrically couple an upper diffusion region with a lower diffusion region. A hammer head 204 is included on the end of polysilicon line 202 to compensate for the line end shortening. As is illustrated in the bottom portion of FIG. 2, these additional features can effectively compensate for line end shortening in some situations.

These additional features are typically added to a layout automatically during a process known as optical proximity correction (OPC). For example, FIG. 3 illustrates line end geometry 302 (solid line) prior to OPC and the resulting corrected line end geometry 304 after OPC (dashed line). Note that the corrected line end geometry 304 includes regions with a positive edge bias in which the size of the original geometry 302 is increased, as well as regions of negative edge bias in which the size of the original geometry 302 is decreased.

Performing an operation, such as OPC, can be extremely time-consuming, because the operation typically involves numerous iterations of a time-consuming modeling and correction process. Furthermore, the operation must be applied to all of the cells that comprise a layout of an integrated circuit.

In order to speed up operations such as OPC, existing systems often perform hierarchical processing on a layout to identify identical cells that have the same surrounding environment. (Within this specification and the associated claims, the term “cell” refers to a unit of design, such as an arbitrary geometric region or potion of the layout.) If such identical instances of cells are identified, the existing systems can use a solution computed for one cell as a solution for all other identical instances of the cell. This saves a great deal of time for layouts that contain many instances of the same cell.

Unfortunately, existing systems cannot reuse solutions in cases where identical cells have different surrounding environments, or when a layout of a given cell differs only slightly from the layout of another cell.

Moreover, existing systems do a poor job of distributing the workload involved in computing solutions for cells across multiple processing nodes that are typically available in high-performance computing systems.

What is needed is a method and an apparatus that reuses a solution for a given cell in computing a solution for a cell with a different environment and/or a slightly different layout.

SUMMARY

Embodiments of the present invention provide a system for speeding up an iterative process that simulates and corrects a layout of a target cell within an integrated circuit. In some of these embodiments, the system is a computer system including a CPU.

The system starts by determining if the target cell differs from a preceding cell by less than a predetermined amount or an environment surrounding the preceding cell differs from an environment surrounding the target cell by less than the predetermined amount. If so, the system uses a previously calculated solution for the preceding cell as an initial input to the iterative process for the target cell. Otherwise the system uses the layout of the target cell as the initial input to the iterative process for the target cell. During the iterative process, the system performs one or more repetitions of simulating a current solution to produce a final solution for the target cell.

In some embodiments, during the iterative process, if a simulated layout of a current solution differs from a desired layout by less than a pre-specified amount, the system accepts the current solution as the final solution for the target cell. Otherwise, the system corrects the current solution to compensate for differences between the simulated layout and the desired layout.

In some embodiments, when determining if the target cell differs from the preceding cell by less than the predetermined amount, the system determines if: (1) the layout of the target cell and a layout of the preceding cell match, but an environment surrounding the target cell differs from an environment surrounding the preceding cell, (2) the layout of the target cell and the layout of the preceding cell match and the environment surrounding the target cell and the environment surrounding the preceding cell match, or (3) the layout of the target cell and the layout of the preceding cell differ by less than a pre-specified amount

In some embodiments, if the layout of the target cell matches the layout of the preceding cell, but the environment surrounding the target cell differs from the environment surrounding the preceding cell, the system performs the iterative process for features within a border region in the target cell that can be affected by the environment surrounding the target cell, but ignores features within the target cell that are not located within the border region.

In some embodiments, if the previously calculated solution for the preceding cell is used as the initial input for the iterative process, and if the iterative process produces a simulation result that differs significantly from a desired layout, the system restarts the iterative process using the desired layout instead of the previously calculated solution as the initial input to the iterative process.

In some embodiments, prior to considering the target cell, the system receives a specification for the layout of the integrated circuit and divides the layout into a plurality of cells, whereby each cell can be independently subjected to the iterative process.

In some embodiments, when performing the iterative process, the system performs a model-based optical proximity correction (OPC).

Embodiments of the present invention provide a computer-readable storage medium storing instructions that when executed by a computer cause the computer to perform a method for speeding up an iterative process that simulates and corrects a layout of a target cell within an integrated circuit. In these embodiments, when performing the method, the computer first determines if the target cell differs from a preceding cell by less than a predetermined amount or an environment surrounding the preceding cell differs from an environment surrounding the target cell by less than the predetermined amount. If so, the computer uses a previously calculated solution for the preceding cell as an initial input to the iterative process for the target cell. Otherwise the computer uses the layout of the target cell as the initial input to the iterative process for the target cell. During the iterative process, the computer performs one or more repetitions of simulating a current solution to produce a final solution for the target cell.

Embodiments of the present invention provide an apparatus for speeding up an iterative process that simulates and corrects a layout of a target cell within an integrated circuit. The apparatus includes at least one central processing unit (CPU). During operation, the CPU is configured to determine if the target cell differs from a preceding cell by less than a predetermined amount or an environment surrounding the preceding cell differs from an environment surrounding the target cell by less than the predetermined amount. If so, the CPU is configured to use a previously calculated solution for the preceding cell as an initial input to the iterative process for the target cell. Otherwise, the CPU is configured to use the layout of the target cell as the initial input to the iterative process for the target cell. During the iterative process, the CPU is configured to perform one or more repetitions of simulating a current solution to produce a final solution for the target cell

BRIEF DESCRIPTION OF THE FIGURES

FIG. 1 illustrates the line end shortening problem.

FIG. 2 illustrates the use of a hammerhead to compensate for the line end shortening problem.

FIG. 3 illustrates a line end prior to and after optical proximity correction.

FIG. 4 is a flow chart illustrating the wafer fabrication process in accordance with an embodiment of the invention.

FIG. 5 illustrates the process of creating a mask to be used in fabricating an integrated circuit in accordance with an embodiment of the invention.

FIG. 6 illustrates an iterative process, such as OPC, involving simulation and correction in accordance with an embodiment of the invention.

FIG. 7 is a flow chart illustrating the processing of a target cell in accordance with an embodiment of the invention.

FIG. 8 is illustrates the border region and the interior of a cell in accordance with an embodiment of the invention.

FIG. 9 is a flow chart illustrating the processing of a target cell in accordance with another embodiment of the invention.

DETAILED DESCRIPTION Wafer Fabrication Process

FIG. 4 is a flow chart illustrating the wafer fabrication process in accordance with an embodiment of the invention. The system starts by applying a photoresist layer to the top surface of a wafer (step 402). Next, the system bakes the photoresist layer (step 404). The system then positions a mask over the photoresist layer (step 406), and exposes the photoresist layer through the mask (step 408). Next, the system optionally bakes the wafer again (step 414) before developing the photoresist layer (step 416). Next, either a chemical etching or ion implantation step takes place (step 418) before the photoresist layer is removed (step 420). (Note that in the case of a lift-off process, a deposition can take place.) Finally, a new layer of material can be added and the process can be repeated for the new layer (step 422).

Design Process

FIG. 5 illustrates the process of creating a mask to be used in the wafer fabrication process described above in accordance with an embodiment of the invention. The process starts when a circuit designer produces a design 502 in VHDL, or some other hardware description language. VHDL is an acronym for VHSIC Hardware Description Language. (VHSIC is a Department of Defense acronym that stands for very high-speed integrated circuits.) The VHDL standard has been codified in Institute for Electrical and Electronic Engineers (IEEE) standard 1076-1993.

Layout 502 then feeds through a layout system that performs a number of functions, such as synthesis 504, placement and routing 506 and verification 508. The result is an integrated circuit (IC) layout 510, which is in the form of a hierarchical specification expressed in a format such as GDSII.

IC layout 510 then passes into OPC post-processing system 511, which performs optical proximity corrections to compensate for optical effects that arise during the photolithography process.

The output of OPC post-processing system 511 is a new IC layout 518. New IC layout 518 subsequently passes into mask fabrication and inspection processes 520.

Iterative Process

FIG. 6 illustrates an iterative process, such as OPC, involving simulation and correction in accordance with an embodiment of the invention. Prior to the iterative process, IC layout 510 feeds into a hierarchical processor 602, which divides IC layout 510 into cells. (Note that hierarchical processor 602 can be implemented on, a single CPU, a process that can run on different CPUs, or a number of processes that can run on multiple CPUs.) Hierarchical processor 602 then distributes the cells to one or more processors to perform the iterative process. In a single CPU embodiment, one of the processors, e.g. the processor 622, may be the same physical CPU as the hierarchical processor 602. The simulation and correction loop on the right-hand side of FIG. 6 illustrates the operation of one such processor (e.g. the processor 622). However, note that hierarchical processor 602 can also communicate with other processors 620-622 that operate in parallel, for example as part of a distributed computing cluster.

Note that unlike in existing systems, processor 622 feeds both a desired cell layout 604 and a proposed solution 606 for a target cell into simulation unit 608. For example, the proposed solution 606 could be the post-OPC layout for a different cell that had a similar initial layout to the current cell, e.g. the desired cell layout 604. The process of selecting this proposed solution 606 is discussed in more detail with reference to FIG. 7 below. Additional shared storage (not shown) may be used to track prior solutions and hash codes as described below. In one embodiment, hierarchical processor 602 stores prior solutions and hash codes. In another embodiment, a separate processor is dedicated to answering requests for prior solutions.

The system then simulates the proposed solution 606 in simulation unit 608 to produce a simulation result for that layout. Next, this simulation result is verified in box 610 to determine if the manufactured result, as determined by simulation, (or “simulated result”) is close enough to the desired cell layout 604 within a pre-specified tolerance, e.g. is it a match. If so, the process is complete and the solution is returned to hierarchical processor 602 to be included in new IC layout 518. Note, in some instances the solution is returned by simply indicating that a given cell can reuse an earlier cell's result with a specific orientation. This provides additional data volume savings.

Otherwise, the system corrects the solution 612 to compensate for differences between the then current solution and the desired cell layout 604. The corrected solution is then fed back into simulation unit 608 to repeat the process.

Note that by starting with a proposed solution 606 for a similar cell, fewer iterations of this process are typically needed to produce a solution for the target cell. This is because the first simulation is usually the most time-consuming because all edges must be considered. Subsequent simulations of similar cells merely have to correct previous simulations results in the proposed solution that were produced during the first simulation. Moreover, the proposed solution can include simulation results cached from a previous run through step 608, thereby saving even more time. Note that if the proposed solution is too far out of specification, the system simply starts the simulation over and disregards the proposed solution. Also note that if a solution can be reused for more than one cell, the size of the output file 518 can be reduced.

Processing a Cell Using a Suggested Solution

FIG. 7 is a flow chart illustrating the processing of a cell using a suggested solution in accordance with an embodiment of the invention. The system starts by determining if the target cell is similar to a preceding cell for which a previously calculated solution already exists (step 702). This operation may involve accessing a database containing specifications for preceding cells.

In one embodiment, hierarchical processor 602 maintains such a database of cells and can be queried by the processors, e.g. processor 622.

In one embodiment of the invention, a preceding cell is similar to a target cell if the layout of the target cell matches the layout of the preceding cell, even if the environment surrounding the target cell differs from the environment surrounding the preceding cell.

In another embodiment of the invention, the target cell is similar to the preceding cell if the layout of the target cell differs from the layout of the preceding cell by less than a pre-specified amount.

If at step 704 the target cell is not similar to a preceding cell, the system uses the layout of the target cell itself as the proposed solution 606 for the iterative process (step 708).

Otherwise, if the target cell is similar to a preceding cell at step 704, the system uses the previously calculated solution for the preceding cell as the proposed solution 606 for the iterative process (step 706).

During the iterative process, if the simulation result of the previously calculated solution differs from the desired cell layout 604 by more than a pre-specified amount, the system ignores the previously calculated solution and restarts the iterative process using the layout of the target cell as the proposed solution 606 (step 710).

Referring to the layout of target cell 800 in FIG. 8, note that if the layout of target cell 800 matches the layout of a preceding cell and only the cell environments differ, the iterative process only has to consider features within a border region 802 of target cell 800 that are close to the boundary of target cell 800 and can consequently be affected by the environment surrounding target cell 800. The system can ignore features in the interior 804 of target cell 800 that cannot be affected by the environment surrounding target cell 800.

Process of Using a Hash Code to Identify an Identical Cell

FIG. 9 is a flow chart illustrating the processing of a target cell in accordance with another embodiment of the invention. The system starts by performing an overlap removal operation for features in the target cell (step 902). Next, the system generates a hash code for the target cell using various geometric properties of the cell (step 903). For example, some embodiments make use of the figure count, the edge count, the area, the perimeter, other properties, and/or combinations of properties to generate the hash code. This can be accomplished by using any one of a large number of well-known hash functions on the layout of the target cell after overlap removal has been performed.

Next, the system determines if the hash code for the target cell matches a hash code for another cell for which there exists a previously computed solution (step 904). This operation may involve accessing a database of containing specifications of preceding cells.

If at step 906 the hash code for the target cell does not match a hash code for a preceding cell, the system processes the target cell to produce a solution for the target cell (step 908). Note that this processing operation can include any type of operation that can be performed on cells in a layout for an integrated circuit. For example, the processing operation can involve data fracturing, model-based optical proximity correction (OPC), rule-based optical proximity correction, or phase shifter assignment for the target cell.

Otherwise, if at step 906 the hash code for the target cell matches a hash code for a preceding cell, the system compares the complete layout of the target cell with the complete layout of the preceding cell to ensure that the target cell is identical to the preceding cell (step 910).

If at step 912 these do not match, the system processes the target cell to produce a solution for the target cell (step 908).

Otherwise, if at step 912 the complete layouts match, the system uses the previously calculated solution for the preceding cell as a solution for the target cell (step 914).

Note that instead of (or in addition to) comparing hash codes, cells that are likely to be similar can be identified by looking at other cell attributes, such as cell size, cell name, or the number of polygons within a cell.

In one embodiment of the present invention, the above-described process is performed on a multiple processor system or a distributed processing configuration as is illustrated in FIG. 6. Note that such a system can use message passing or shared memory for communications between computing nodes.

The foregoing description is presented to enable one to make and use the invention, and is provided in the context of a particular application and its requirements. Various modifications to the disclosed embodiments will be readily apparent, and the general principles defined herein may be applied to other embodiments and applications without departing from the spirit and scope of the invention. Thus, the invention is not intended to be limited to the embodiments shown, but is to be accorded the widest scope consistent with the principles and features disclosed herein.

The data structures and code described in this detailed description can be stored on a computer readable storage medium, which may be any device or medium that can store code and/or data for use by a computer system. This includes, but is not limited to, magnetic and optical storage devices such as disk drives, magnetic tape, CDs (compact discs) and DVDs (digital versatile discs or digital video discs), and computer instruction signals embodied in a transmission medium (with or without a carrier wave upon which the signals are modulated). For example, the transmission medium may include a communications network, such as the Internet.

Note that the invention can be applied to any type of lithographic process for fabricating semiconductor chips, including processes that make use of, deep-ultraviolet (DUV) radiation, extreme ultraviolet (EUV) radiation, X-rays, and electron beams, along with suitably modified masks.

The foregoing descriptions of embodiments of the invention have been presented for purposes of illustration and description only. They are not intended to be exhaustive or to limit the invention to the forms disclosed. Accordingly, many modifications and variations will be apparent. Additionally, the above disclosure is not intended to limit the invention. The scope of the invention is defined by the appended claims. 

1. A method for speeding up an iterative process that simulates and corrects a layout of a target cell within an integrated circuit, comprising: determining if the target cell differs from a preceding cell by less than a predetermined amount or an environment surrounding the preceding cell differs from an environment surrounding the target cell by less than the predetermined amount; if so, using a previously calculated solution for the preceding cell as an initial input to the iterative process for the target cell; otherwise using the layout of the target cell as the initial input to the iterative process for the target cell; and during the iterative process, performing one or more repetitions of simulating a current solution to produce a final solution for the target cell.
 2. The method of claim 1, wherein during the iterative process, if a simulated layout of a current solution differs from a desired layout by less than a pre-specified amount, accepting the current solution as the final solution for the target cell; otherwise, correcting the current solution to compensate for differences between the simulated layout and the desired layout.
 3. The method of claim 1, wherein determining if the target cell differs from the preceding cell by less than the predetermined amount involves determining if: the layout of the target cell and a layout of the preceding cell match, but an environment surrounding the target cell differs from an environment surrounding the preceding cell, the layout of the target cell and the layout of the preceding cell match and the environment surrounding the target cell and the environment surrounding the preceding cell match, or the layout of the target cell and the layout of the preceding cell differ by less than a pre-specified amount
 4. The method of claim 3, wherein if the layout of the target cell matches the layout of the preceding cell, but the environment surrounding the target cell differs from the environment surrounding the preceding cell, the method further comprises: performing the iterative process for features within a border region in the target cell that can be affected by the environment surrounding the target cell, and ignoring features within the target cell that are not located within the border region.
 5. The method of claim 1, wherein if the previously calculated solution for the preceding cell is used as the initial input for the iterative process, and if the iterative process produces a simulation result that differs significantly from a desired layout, the method further comprises restarting the iterative process using the desired layout instead of the previously calculated solution as the initial input to the iterative process.
 6. The method of claim 1, wherein prior to considering the target cell, the method further comprises: receiving a specification for the layout of the integrated circuit; and dividing the layout into a plurality of cells, whereby each cell can be independently subjected to the iterative process.
 7. The method of claim 1, wherein performing the iterative process involves performing model-based optical proximity correction (OPC).
 8. A computer-readable storage medium storing instructions that when executed by a computer cause the computer to perform a method for speeding up an iterative process that simulates and corrects a layout of a target cell within an integrated circuit, the method comprising: determining if the target cell differs from a preceding cell by less than a predetermined amount or an environment surrounding the preceding cell differs from an environment surrounding the target cell by less than the predetermined amount; if so, using a previously calculated solution for the preceding cell as an initial input to the iterative process for the target cell; otherwise using the layout of the target cell as the initial input to the iterative process for the target cell; and during the iterative process, performing one or more repetitions of simulating a current solution to produce a final solution for the target cell.
 9. The computer-readable storage medium of claim 8, wherein during the iterative process, if a simulated layout of a current solution differs from a desired layout by less than a pre-specified amount, accepting the current solution as the final solution for the target cell; otherwise, correcting the current solution to compensate for differences between the simulated layout and the desired layout.
 10. The computer-readable storage medium of claim 8, wherein determining if the target cell differs from the preceding cell by less than the predetermined amount involves determining if: the layout of the target cell and a layout of the preceding cell match, but an environment surrounding the target cell differs from an environment surrounding the preceding cell, the layout of the target cell and the layout of the preceding cell match and the environment surrounding the target cell and the environment surrounding the preceding cell match, or the layout of the target cell and the layout of the preceding cell differ by less than a pre-specified amount
 11. The computer-readable storage medium of claim 10, wherein if the layout of the target cell matches the layout of the preceding cell, but the environment surrounding the target cell differs from the environment surrounding the preceding cell, the method further comprises: performing the iterative process for features within a border region in the target cell that can be affected by the environment surrounding the target cell, and ignoring features within the target cell that are not located within the border region.
 12. The computer-readable storage medium of claim 8, wherein if the previously calculated solution for the preceding cell is used as the initial input for the iterative process, and if the iterative process produces a simulation result that differs significantly from a desired layout, the method further comprises restarting the iterative process using the desired layout instead of the previously calculated solution as the initial input to the iterative process.
 13. The computer-readable storage medium of claim 8, wherein prior to considering the target cell, the method further comprises: receiving a specification for the layout of the integrated circuit; and dividing the layout into a plurality of cells, whereby each cell can be independently subjected to the iterative process.
 14. The computer-readable storage medium of claim 8, wherein performing the iterative process involves performing model-based optical proximity correction (OPC).
 15. An apparatus for speeding up an iterative process that simulates and corrects a layout of a target cell within an integrated circuit, comprising: at least one central processing unit (CPU); wherein the CPU is configured to determine if the target cell differs from a preceding cell by less than a predetermined amount or an environment surrounding the preceding cell differs from an environment surrounding the target cell by less than the predetermined amount; if so, the CPU is configured to use a previously calculated solution for the preceding cell as an initial input to the iterative process for the target cell; otherwise the CPU is configured to use the layout of the target cell as the initial input to the iterative process for the target cell; and during the iterative process, the CPU is configured to perform one or more repetitions of simulating a current solution to produce a final solution for the target cell.
 16. The apparatus of claim 15, wherein during the iterative process, if a simulated layout of a current solution differs from a desired layout by less than a pre-specified amount, the CPU is configured to accept the current solution as the final solution for the target cell; otherwise, the CPU is configured to correct the current solution to compensate for differences between the simulated layout and the desired layout.
 17. The apparatus of claim 15, wherein when determining if the target cell differs from the preceding cell by less than the predetermined amount, the CPU determines if: the layout of the target cell and a layout of the preceding cell match, but an environment surrounding the target cell differs from an environment surrounding the preceding cell, the layout of the target cell and the layout of the preceding cell match and the environment surrounding the target cell and the environment surrounding the preceding cell match, or the layout of the target cell and the layout of the preceding cell differ by less than a pre-specified amount
 18. The apparatus of claim 17, wherein if the layout of the target cell matches the layout of the preceding cell, but the environment surrounding the target cell differs from the environment surrounding the preceding cell, the CPU is configured to: perform the iterative process for features within a border region in the target cell that can be affected by the environment surrounding the target cell, and ignore features within the target cell that are not located within the border region.
 19. The apparatus of claim 15, wherein if the previously calculated solution for the preceding cell is used as the initial input for the iterative process, and if the iterative process produces a simulation result that differs significantly from a desired layout, the CPU is configured to restart the iterative process using the desired layout instead of the previously calculated solution as the initial input to the iterative process.
 20. The apparatus of claim 15, wherein prior to considering the target cell, the CPU is configured to: receive a specification for the layout of the integrated circuit; and divide the layout into a plurality of cells, whereby each cell can be independently subjected to the iterative process.
 21. The apparatus of claim 15, wherein during the iterative process, the CPU is configured to perform model-based optical proximity correction (OPC). 